Approximate dynamic programming in transportation and logistics: a unified framework

Deterministic optimization has enjoyed a rich place in transportation and logistics, where it represents a mature field with established modeling and algorithmic strategies. By contrast, sequential stochastic optimization models (dynamic programs) have been plagued by the lack of a common modeling framework, and by algorithmic strategies that just do not seem to scale to real-world problems in transportation. This paper is designed as a tutorial of the modeling and algorithmic framework of approximate dynamic programming; however, our perspective on approximate dynamic programming is relatively new, and the approach is new to the transportation research community. We present a simple yet precise modeling framework that makes it possible to integrate most algorithmic strategies into four fundamental classes of policies, the design of which represents approximate solutions to these dynamic programs. The paper then uses problems in transportation and logistics to indicate settings in which each of the four classes of policies represents a natural solution strategy, highlighting the fact that the design of effective policies for these complex problems will remain an exciting area of research for many years. Along the way, we provide a link between dynamic programming, stochastic programming and stochastic search.